
Kate - if you're looking for a genuine non shedding breed ( as opposed to the BYB breeders adverts about dogs that don't shed - when they do) you need to go for a pedigree dog to be honest.
But bear in mind that if you want the convenience of no dog hair, you need to be prepared for loads of grooming. It is totally unfair to keep a poodle (for instance) and not groom it daily. If you're not willing to put in the hard work - give it second thoughts!
And be prepared for 6-8 weekly visits to the dog groomers for clipping. This is not cheap! If you can't clip yourself, it is something that has to be done by someone. But you do need to keep up the grooming youself in between visits. Once matted, and left, the poor dog has no way to alleviate the discomfort that you have caused.
Obviously, poodles are not the only non shedding breed, but do some research first. I am not trying to put you off! :-) But the treasure of this forum, is that you can come and be told the drawbacks as well as the benefits. Personally, I adore Poodles, but I do find grooming therapeutic. Some folk find grooming a chore. Think about which category you fall into! :-)